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A168641 Triangle read by rows: T(n,k) = [x^k] p(x,n), where p(x,n) = 3*(x + 1)^n - 2*(x^n + 1) - n*(x + x^(n - 1)) for n >= 2, p(x,0) = 1, and p(x,1) = x + 1. 4
1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 8, 18, 8, 1, 1, 10, 30, 30, 10, 1, 1, 12, 45, 60, 45, 12, 1, 1, 14, 63, 105, 105, 63, 14, 1, 1, 16, 84, 168, 210, 168, 84, 16, 1, 1, 18, 108, 252, 378, 378, 252, 108, 18, 1, 1, 20, 135, 360, 630, 756, 630, 360, 135, 20, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

Triangle begins:

  1;

  1,  1;

  1,  2,   1;

  1,  6,   6,   1;

  1,  8,  18,   8,   1;

  1, 10,  30,  30,  10,   1;

  1, 12,  45,  60,  45,  12,   1;

  1, 14,  63, 105, 105,  63,  14,   1;

  1, 16,  84, 168, 210, 168,  84,  16,  1;

  1, 18, 108, 252, 378, 378, 252, 108,  18,  1;

  1, 20, 135, 360, 630, 756, 630, 360, 135, 20, 1;

  ...

MATHEMATICA

p[x_, n_] := If[n == 0, 1, If[n == 1, x + 1, 3*(x + 1)^n - (x^n + 1) - (x^n + n*x^(n - 1) + n*x + 1)]];

Flatten[Table[CoefficientList[p[x, n], x], {n, 0, 10}]]

PROG

(Maxima) T(n, k) := ratcoef(if n <= 2 then (1 + x)^n else 3*(x + 1)^n - (x^n + 1) - (x^n + n*x^(n - 1) + n*x + 1), x, k);

create_list(T(n, k), n, 0, 12, k, 0, n); /* Franck Maminirina Ramaharo, Jan 02 2019 */

CROSSREFS

Cf. A132046, A168643, A168644, A168646.

Sequence in context: A166919 A260238 A283795 * A255914 A143185 A157635

Adjacent sequences:  A168638 A168639 A168640 * A168642 A168643 A168644

KEYWORD

nonn,easy,less

AUTHOR

Roger L. Bagula and Gary W. Adamson, Dec 01 2009

EXTENSIONS

Edited by Franck Maminirina Ramaharo, Jan 02 2019

STATUS

approved

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Last modified June 1 02:04 EDT 2020. Contains 334758 sequences. (Running on oeis4.)